

Q1: Can I process the part of the effect after "then" in this card's Your Turn effect without meeting the "by" condition?
No, you can't. If you don't suspend this card, you can't process the part after "then" in its Your Turn effect.
Rei Katsura BT24-087 R App Driver/Appmon [Start of Your Main Phase] If your opponent has a Digimon, gain 1 memory. [Your Turn] When any of your Digimon get linked, by suspending this Tamer, <Draw 1> and trash 1 card in your hand. Then, 1 of your Digimon may app fuse into a Digimon card with the [System], [Life] or [Transmutation] trait in the trash. --- [Security] Play this card without paying the cost.
Rei Katsura BT24-087 R App Driver/Appmon [Start of Your Main Phase] If your opponent has a Digimon, gain 1 memory. [Your Turn] When any of your Digimon get linked, by suspending this Tamer, <Draw 1> and trash 1 card in your hand. Then, 1 of your Digimon may app fuse into a Digimon card with the [System], [Life] or [Transmutation] trait in the trash. --- [Security] Play this card without paying the cost.
Rei Katsura BT24-087 R App Driver/Appmon [Start of Your Main Phase] If your opponent has a Digimon, gain 1 memory. [Your Turn] When any of your Digimon get linked, by suspending this Tamer, <Draw 1> and trash 1 card in your hand. Then, 1 of your Digimon may app fuse into a Digimon card with the [System], [Life] or [Transmutation] trait in the trash. --- [Security] Play this card without paying the cost.
桂レイ BT24-087 R アプリドライヴァー/アプモン 【自分のメインフェイズ開始時】相手のデジモンがいるなら、メモリー+1。 【自分のターン】自分のデジモンがリンクしたとき、このテイマーをレストさせることで、≪1ドロー≫し、自分の手札1枚を破棄する。その後、自分のデジモン1体をトラッシュの特徴に「システム」/「ライフ」/「変化」を持つデジモンカードにアプ合体できる。 --- 【セキュリティ】このカードをコストを支払わずに登場させる。